CN106650278A - Method for calculating stable orbit of non-synchronous binary star system - Google Patents

Abstract

The invention relates to a method for calculating a stable orbit of a non-synchronous binary star system, in particular to a method for calculating the stable orbit of the non-synchronous binary star system based on second-order differential correction, belongs to the field of aerospace technologies and is suitable for orbit design for detection of the non-synchronous binary star system by a detector. For an arbitrary non-synchronous binary star system, the system is firstly considered as a synchronous system for periodic orbit searching; then the synchronous system is converted into a non-synchronous system according to a spin period of minor planets, and the obtained periodic orbit is divided into a plural sections according to an orbital period; the plural sections of the periodic orbit are introduced into the non-synchronous system for orbit integral; the plural sections of the orbit are respectively subject to position correction and speed correction; and the long-term stable orbit in the non-synchronous system is obtained through multiple iterations. The stable orbit suitable for the non-synchronous binary star system can be realized, an initial value of the orbit is easy to select and good in convergence, and the calculation efficiency is high.

Description

The stable orbit computational methods of asynchronous binary-star system

Technical field

The present invention relates to a kind of orbit computation method of asynchronous binary-star system, more particularly to one kind are repaiied based on second-order differential The computational methods of positive asynchronous binary-star system stable orbit, belong to field of aerospace technology, it is adaptable to which detector is to non-same The Track desigh that step binary-star system is detected.

Background technology

Binary asteroid system is a special class asteroid, and system is mutually constituted by two around the circular asteroid of barycenter, The barycenter of simultaneity factor runs around the sun.Binary asteroid is large number of, constitutes about near-Earth asteroid and main belt asteroids number The 16% of amount.There is special science to return to carry out detection mission to binary-star system, can be with the evolution of Study system and power Formation mechenism is learned, YORP effects are verified.Further, since the characteristic of binary-star system itself, the physical parameter of system can be using ground Face is observed and being estimated, effectively reduces the difficulty of detection mission, therefore it is following survey of deep space to carry out detection to binary-star system One of focus.Spin and revolution state according to binary-star system, can be divided into double synchronization systems by system, single synchronization system and Asynchronous system, wherein the roll rate of two components and the orbit angular velocity of relative motion are identical in double synchronization systems, Dan Tong The roll rate of one of step system neutron star is identical with orbit angular velocity, and the roll rate and track of asynchronous system neutron star Angular speed is differed, wherein asynchronous binary-star system ratio highest shared in systems.Circular detection to binary-star system It is the important component part of ASTEREX.In the design of detection mission, need to be designed the track near double star, search for Stable orbit in system will be the basis of task design.

At present in the searching method of binary-star system inner orbit, first technology【1】(referring to Haibing Shang, Xiaoyu Wu,Pingyuan Cui.Periodic orbits in the doubly synchronous binary asteroid system and their applications in space missions[J].Astrophys Space Sci,2014, 355:2154.) based on double ellipsoidal models, to double synchronous binary-star systems, nearby track is studied, and is acquired greatly using symmetry Amount can be used for the periodic orbit for detecting.But the method is only applicable to double synchronization systems, for spin and the nonsynchronous system of revolution Will be inapplicable.

First technology【2】(referring to Qiao Dong, Li Xiangyu, Cui Pingyuan etc., based on speed Poincare section binary asteroid system week Phase track searching method, CN104477411A) periodic orbit is scanned for using speed Poincaré map, by mapping through The position of X-axis can obtain corresponding periodic orbit.The method is equally only applicable to the binary-star system of spin locking, same for non- The system of step will be inapplicable.

The content of the invention

The purpose of the present invention is to propose to a kind of stable orbit computational methods suitable for asynchronous binary-star system, the method elder generation Based on synchronous binary-star system calculating cycle track, then the periodic orbit in synchronization system is transformed into asynchronous binary-star system In, orbit integration is carried out, track steady in a long-term is obtained using second-order differential correction algorithm, easily choose with initial value, convergence The features such as good.

The purpose of the present invention is achieved through the following technical solutions.

The stable orbit computational methods of asynchronous binary-star system disclosed by the invention.It is first to any asynchronous binary-star system System is thought of as into synchronization system carries out periodic orbit search, is then converted to synchronization system according to asteroidal self-rotary cycle Asynchronous system and obtain periodic orbit be divided into some sections by the orbital period, bringing into asynchronous system carries out orbit integration, Position correction and speed amendment are carried out to some sections of tracks using second-order differential amendment, asynchronous system is obtained by successive ignition In track steady in a long-term.Can realize be applied to asynchronous binary-star system stable orbit, and the track race for obtaining it is many, restrain Property it is good, computational efficiency is high.

The stable orbit computational methods of asynchronous binary-star system disclosed by the invention, comprise the following steps：

Step one, according to determine target binary-star system parameter, ignore spin angle velocity difference, binary-star system is thought of as Synchronous binary-star system, sets up ellipsoid-ellipsoidal binary system model, and under barycenter rotating coordinate system kinetic model is set up.It is described The shape of binary-star system parameter including double star, mass ratio and relative distance.

Wherein ρ represents detector to the position vector of barycenter, ω for system angular velocity of rotation, ρ₁And ρ₂Arrive for detector Double star primary and the position vector of component.U₁, U₂Represent the gravitational potential energy of double star：

Wherein α, beta, gamma for celestial body three main axis lengths, r₁,r₂For position of two celestial bodies under barycenter rotating coordinate system Vector.

Step 2, periodic orbit search is carried out to synchronous binary-star system, periodic orbit is obtained by corresponding searching method Race.

Periodic orbit in synchronous binary-star system meets The original state of periodic orbit can be simplified using the symmetry of binary-star system model；The track symmetrical for face, rail Road meets from OXZ planes, initial valueMeet after half orbital period Axisymmetric track, track meets from X-axis, initial valueShould meet after half orbital periodThe region in binary-star system is scanned for according to existing searching method obtain different track weeks Phase and the periodic orbit race of orbital energy.

Existing searching method is included using speed Poincaré map or grid search.

Step 3, according to the roll rate of binary-star system, set up the kinetics equation of asynchronous system.

Two asteroidal roll rates are respectively ω₁,ω₂, initial spin angle is θ₁,θ₂, then under barycenter rotation system Roll rate is respectively ω '₁=ω₁-ω₀, ω '₂=ω₂-ω₀, spin angle is over time φ₁=θ₁+ω′₁T, φ₂ =θ₂+ω′₂T, then kinetics equation (1) be changed into,

Wherein R_zFor spin matrix about the z axis.

Step 4, the periodic orbit race for obtaining step 2 are divided into some sections according to the cycle, and the initial value for taking each section is brought into Formula (6) is integrated, and the speed of track is modified, it is ensured that the position of each section of track keeps continuous in asynchronous system.

The initial value of per section of note is X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi], the initial integration time of every section of track isWherein T is the orbital period, and n is segments, can improve convergence according to arbitrarily selection, increase n But reduce calculating speed.

Differential update equation：

Wherein δ X_i=[0,0,0, δ v_xi,δv_yi,δv_zi], δ X_i+1=[0,0,0, δ v_xi+1,δv_yi+1,δv_zi+1]

State for initial equilibrium state to last current state is shifted Matrix.δv_xi+1=v_xi+1-v_x′i+1,δy_i+1=y_i+1-y′_i+1,δz_i+1=z_i+1-z′_i+1。

X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] press kinetics equation (6) integration t_iFinal value after time is X '_i+1=[x '_i+1, y′_i+1,z′_i+1,v′_xi+1,v′_yi+1,v′_zi+1]。

Formula (8) can be expressed as：

So as to be modified to every section of initial value, initial value is changed into X_i+δX_i。

Position correction is carried out respectively to every track section, new initial velocity is obtained, initial position is constant.

Step 5, the initial position of every section of track and the time of integration described in step 4 are modified, make each section of speed Keep in asynchronous system continuous.

To initial value X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] speed amendment depend on X simultaneously_i-1=[x_i-1,y_i-1,z_i-1, v_xi-1,v_yi-1,v_zi-1] and X_i+1=[x_i+1,y_i+1,z_i+1,v_xi+1,v_yi+1,v_zi+1] situation.

Wherein V_i=[v_xi,v_yi,v_zi], R_i=[x_i,y_i,z_i], V_i ^-Represent from X_i-1The speed that forward direction integration is obtained, and V_i ⁺Table Show from X_i+1Inversely integrate the speed for obtaining.

Speed amendment is carried out to every track section by formula (10), new initial position and every section of time of integration is obtained.

Step 6, each section of interorbital position of calculating and velocity deviation, if being less than a certain value, then it is assumed that track is continuous, i.e., Track of the stable operation in asynchronous system is obtained, otherwise repeat step four and five, until meet the constraint.

The each fragment position error of track and velocity error of the new amendment of note is δ r_iWith δ v_i, the total site error of track is designated asGeneral speed error is designated asIf δ is R ＜ ε₁And δ V ＜ ε₂ Then think that track is continuous, as stable orbit, ε₁,ε₂For a small amount of, preferably ε₁=10^-5M, ε₂=10^-3M/s, can be according to little row The size of star and task precision are adjusted.The repeat step four and five if constraint is unsatisfactory for, by successive ignition stable rail is obtained Road.

Beneficial effect：

1st, the stable orbit computational methods of a kind of asynchronous binary-star system disclosed by the invention, obtain first asynchronous double Stable orbit in star system, can be used as the mission orbit of detection mission.

2. stable orbit computational methods of a kind of asynchronous binary-star system disclosed by the invention, synchronous binary-star system calculate The periodic orbit for obtaining easily is obtained as initial value, initial value.

2nd, the stable orbit computational methods of a kind of asynchronous binary-star system disclosed by the invention, by by track section, dividing Position correction and speed amendment are not carried out, the convergence of track is improve, track convergence is high.

Description of the drawings

A kind of stable orbit computational methods schematic flow sheet of the asynchronous binary-star system of Fig. 1 present invention；

Periodic orbit under Fig. 2 synchronization binary-star systems；

The asynchronous binary-star system rotating coordinate system schematic diagrames of Fig. 3；

Fig. 4 segmented tracks position correction schematic diagrames；

Fig. 5 segmented tracks speed amendment schematic diagrames；

Stable orbit under the asynchronous binary-star system that Fig. 6 present invention is obtained.

Specific embodiment

In order to better illustrate objects and advantages of the present invention, below in conjunction with the accompanying drawings the content of the invention is done further with example Explanation.

Embodiment 1：

The stable orbit computational methods of a kind of asynchronous binary-star system of the present embodiment, comprise the following steps：

Step one, according to determine target binary-star system parameter, ignore spin angle velocity difference, binary-star system is thought of as Synchronous binary-star system, sets up ellipsoid-ellipsoidal binary system model, and under barycenter rotating coordinate system kinetic model is set up.It is described The shape of binary-star system parameter including double star, mass ratio and relative distance.

Wherein ρ represents detector to the position vector of barycenter, ω for system angular velocity of rotation, ρ₁And ρ₂Arrive for detector Double star primary and the position vector of component.U₁, U₂Represent the gravitational potential energy of double star：

Wherein α, beta, gamma for celestial body three main axis lengths, r₁,r₂For position vector of two celestial bodies under coordinate system.

If three axial lengths of primary are respectively 0.6124km, 0.6km, 0.5880km in binary-star system；Three axial lengths of component point Not Wei 0.5530km, 0.5364km, 0.5300km, quality constant μ=0.4083 of system, orbital period 13.8936h, track Angular velocity omega=1.2562 × 10^-4rad/s。

Step 2, periodic orbit search is carried out to synchronous binary-star system, periodic orbit is obtained by corresponding searching method Race.

Periodic orbit in synchronous binary-star system meets The original state of periodic orbit can be simplified using the symmetry of binary-star system model；The track symmetrical for face, rail Road meets from OXZ planes, initial valueMeet after half orbital period Axisymmetric track, track meets from X-axis, initial valueShould meet after half orbital periodThe region in binary-star system is scanned for according to existing searching method obtain different track weeks Phase and the periodic orbit race of orbital energy.

Existing searching method is included using speed Poincaré map or grid search.The synchronization obtained based on grid search Periodic orbit under system is as shown in Figure 2.

Step 3, according to the roll rate of binary-star system, set up the kinetics equation of asynchronous system.

Take asteroidal self-rotary cycle and be respectively 6.9468h and 12.0545h, initial spin angle is θ₁=0 °, θ₂= 0 °, then rotate the roll rate under system in barycenter and be respectively ω '₁=ω₁-ω₀=1.2562rad/s, ω '₂=ω₂-ω₀= 1.9167×10^-5Rad/s, then kinetics equation (1) be changed into,

Wherein R_zFor spin matrix about the z axis.

Asynchronous binary-star system is as shown in Figure 3 in the schematic diagram that barycenter is rotated under system.

Step 4, the periodic orbit race for obtaining step 2 are divided into some sections according to the cycle, and the initial value for taking each section is brought into Formula (6) is integrated, and the speed of track is modified, it is ensured that the position of each section of track keeps continuous in asynchronous system.

The initial value of per section of note is X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi], the initial integration time of every section of track isWherein T is the orbital period, and n is segments, can improve convergence according to arbitrarily selection, increase n But reduce calculating speed.

Differential update equation：

Wherein δ X_i=[0,0,0, δ v_xi,δv_yi,δv_zi], δ X_i+1=[0,0,0, δ v_xi+1,δv_yi+1,δv_zi+1]

State for initial equilibrium state to last current state is shifted Matrix.δv_xi+1=v_xi+1-v_x′i+1,δy_i+1=y_i+1-y′_i+1,δz_i+1=z_i+1-z′_i+1。

X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] press kinetics equation (6) integration t_iFinal value after time is X '_i+1=[x '_i+1, y′_i+1,z′_i+1,v′_xi+1,v′_yi+1,v′_zi+1]。

Formula (8) can be expressed as：

So as to be modified to every section of initial value, initial value is changed into X_i+δX_i。

Position correction is carried out respectively to every track section, new initial velocity is obtained, initial position is constant, and position correction is shown It is intended to as shown in Figure 4.

Step 5, the initial position of every section of track and the time of integration described in step 4 are modified, make each section of speed Keep in asynchronous system continuous.

To initial value X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] speed amendment depend on X simultaneously_i-1=[x_i-1,y_i-1,z_i-1, v_xi-1,v_yi-1,v_zi-1] and X_i+1=[x_i+1,y_i+1,z_i+1,v_xi+1,v_yi+1,v_zi+1] situation.

Wherein V_i=[v_xi,v_yi,v_zi], R_i=[x_i,y_i,z_i], V_i ^-Represent from X_i-1The speed that forward direction integration is obtained, and V_i ⁺Table Show from X_i+1Inversely integrate the speed for obtaining.

Speed amendment is carried out to every track section by formula (10), new initial position and every section of time of integration, speed is obtained The schematic diagram of degree amendment is as shown in Figure 5.

Step 6, each section of interorbital position of calculating and velocity deviation, if being less than a certain value, then it is assumed that track is continuous, i.e., Track of the stable operation in asynchronous system is obtained, otherwise repeat step four and five, until meet the constraint.

The each fragment position error of track and velocity error of the new amendment of note is δ r_iWith δ v_i, the total site error of track is designated asGeneral speed error is designated asIf δ is R ＜ ε₁And δ V ＜ ε₂ Then think that track is continuous, as stable orbit, ε₁,ε₂For a small amount of, preferably ε₁=10^-5M, ε₂=10^-3M/s, can be according to little row The size of star and task precision are adjusted.The repeat step four and five if constraint is unsatisfactory for, by successive ignition stable rail is obtained Road.The stable orbit obtained after successive ignition is as shown in Figure 6.

Above-described specific descriptions, purpose, technical scheme and the beneficial effect to inventing has been carried out further specifically It is bright, should be understood that the specific embodiment that the foregoing is only the present invention, the protection model being not intended to limit the present invention Enclose, all any modification, equivalent substitution and improvements within the spirit and principles in the present invention, done etc. should be included in the present invention Protection domain within.

Claims (7)

1. stable orbit computational methods of asynchronous binary-star system, it is characterised in that：Comprise the following steps：

Step one, according to determine target binary-star system parameter, ignore spin angle velocity difference, binary-star system is thought of as into synchronization Binary-star system, sets up ellipsoid-ellipsoidal binary system model, and under barycenter rotating coordinate system kinetic model is set up；Described is double Star system parameter includes shape, mass ratio and the relative distance of double star；

$\stackrel{\·\·}{\mathrm{\ρ}}+2\mathrm{\ω}\×\stackrel{\·}{\mathrm{\ρ}}+\mathrm{\ω}\×\mathrm{\ω}\×\mathrm{\ρ}+\stackrel{\·}{\mathrm{\ω}}\×\mathrm{\ρ}=\frac{\∂U_1}{\∂{\mathrm{\ρ}}_1}+\frac{\∂U_2}{\∂{\mathrm{\ρ}}_2}---\left(1\right)$

Wherein ρ represents detector to the position vector of barycenter, ω for system angular velocity of rotation, ρ₁And ρ₂It is detector to double star Primary and the position vector of component；U₁, U₂Represent the gravitational potential energy of double star：

$\left\{\begin{array}{c}{U}_1=(1-\mathrm{\μ})U_e(\mathrm{\ρ}-r_1,{\mathrm{\α}}_1,{\mathrm{\β}}_1,{\mathrm{\γ}}_1)\\ U_2={\mathrm{\μU}}_e(\mathrm{\ρ}-r_2,{\mathrm{\α}}_2,{\mathrm{\β}}_2,{\mathrm{\γ}}_2)\end{array}\right.---\left(2\right)$

$U_e\left(R\right)=\frac{3}{4}{\∫}_{\mathrm{\λ}\left(r\right)}^{\mathrm{\∞}}\mathrm{\φ}(R,v)\frac{d\mathrm{\υ}}{\mathrm{\Δ}\left(\mathrm{\υ}\right)}---\left(3\right)$

$\mathrm{\φ}(R,\mathrm{\υ})=1-\frac{x^2}{\mathrm{\υ}+\mathrm{\α}}-\frac{y^2}{\mathrm{\υ}+{\mathrm{\β}}^2}-\frac{z^2}{\mathrm{\υ}+{\mathrm{\γ}}^2}---\left(4\right)$

$\mathrm{\Δ}\left(\mathrm{\υ}\right)=\sqrt{(\mathrm{\υ}+\mathrm{\α})(\mathrm{\υ}+{\mathrm{\β}}^2)(\mathrm{\υ}+{\mathrm{\γ}}^2)}---\left(5\right)$

Wherein α, beta, gamma for celestial body three main axis lengths, r₁,r₂The position for being two celestial bodies under barycenter rotating coordinate system arrow Amount；

Step 2, periodic orbit search is carried out to synchronous binary-star system, periodic orbit race is obtained by searching method；

Step 3, according to the roll rate of binary-star system, set up the kinetics equation of asynchronous system；

Two asteroidal roll rates are respectively ω₁,ω₂, initial spin angle is θ₁,θ₂, then the spin under system is rotated in barycenter Speed is respectively ω '₁=ω₁-ω₀, ω '₂=ω₂-ω₀, spin angle is over time φ₁=θ₁+ω′₁T, φ₂=θ₂+ ω′₂T, then kinetics equation (1) be changed into,

$\stackrel{\·\·}{\mathrm{\ρ}}+2\mathrm{\ω}\×\stackrel{\·}{\mathrm{\ρ}}+\mathrm{\ω}\×\mathrm{\ω}\×\mathrm{\ρ}+\stackrel{\·}{\mathrm{\ω}}\×\mathrm{\ρ}=R_z\left({\mathrm{\φ}}_1\right(t\left)\right)\frac{\∂U_1}{\∂{\mathrm{\ρ}}_1}+R_z\left({\mathrm{\φ}}_2\right(t\left)\right)\frac{\∂U_2}{\∂{\mathrm{\ρ}}_2}---\left(6\right)$

Wherein R_zFor spin matrix about the z axis；

$R_z\left(\mathrm{\φ}\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& cos\mathrm{\φ}& -\sin \mathrm{\φ}\\ 0& sin\mathrm{\φ}& \cos \mathrm{\φ}\end{array}\right]---\left(7\right)$

Step 4, the periodic orbit race for obtaining step 2 are divided into some sections according to the cycle, and the initial value for taking each section brings formula (6) into It is integrated, the speed of track is modified, it is ensured that the position of each section of track keeps continuous in asynchronous system；To each Section track carries out respectively position correction, obtains new initial velocity, and initial position is constant；

Step 5, the initial position of every section of track and the time of integration described in step 4 are modified, make each section of speed non- Keep in synchronization system continuous；Speed amendment is carried out to every track section, new initial position and every section of time of integration is obtained；

Step 6, each section of interorbital position of calculating and velocity deviation, if being less than a certain value, then it is assumed that track is continuous, that is, obtain Track of the stable operation in asynchronous system, otherwise repeat step four and five, until meet the constraint.

2. stable orbit computational methods of asynchronous binary-star system as claimed in claim 1, it is characterised in that：Step 4 is to rail The method that the speed in road is modified is：

The initial value of per section of note is X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi], the initial integration time of every section of track isWherein T is the orbital period, and n is segments, can improve convergence according to arbitrarily selection, increase n But reduce calculating speed；

Differential update equation：

${\mathrm{\δX}}_{i+1}=\frac{\∂X}{\∂X_0}{|}_{t_i}{\mathrm{\δX}}_i---\left(8\right)$

Wherein δ X_i=[0,0,0, δ v_xi,δv_yi,δv_zi], δ X_i+1=[0,0,0, δ v_xi+1,δv_yi+1,δv_zi+1]

For the state-transition matrix of initial equilibrium state to last current state； δv_xi+1=v_xi+1-v_x′i+1,δy_i+1=y_i+1-y′_i+1,δz_i+1=z_i+1-z′_i+1；

X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] press kinetics equation (6) integration t_iFinal value after time is X '_i+1=[x '_i+1,y ′_i+1,z′_i+1,v′_xi+1,v′_yi+1,v′_zi+1]；

Formula (8) can be expressed as：

${\mathrm{\δX}}_i={\left(\frac{\∂X}{\∂X_0}{|}_{t_i}\right)}^{-1}{\mathrm{\δX}}_{i+1}---\left(9\right)$

So as to be modified to every section of initial value, initial value is changed into X_i+δX_i；

Position correction is carried out respectively to every track section, new initial velocity is obtained, initial position is constant.

3. stable orbit computational methods of asynchronous binary-star system as claimed in claim 1, it is characterised in that：Step 5 is to step The method that the initial position of every section of track and the time of integration described in rapid four are modified is：

To initial value X_i=[x_i,y_i,z_i,v_xi,v_yi,v_zi] speed amendment depend on X simultaneously_i-1=[x_i-1,y_i-1,z_i-1,v_xi-1, v_yi-1,v_zi-1] and X_i+1=[x_i+1,y_i+1,z_i+1,v_xi+1,v_yi+1,v_zi+1] situation；

${\mathrm{\δ\ΔV}}_i=\[\begin{array}{cccccc}{\mathrm{\Φ}}_{R_i}^{-}& {\mathrm{\Φ}}_{t_i}^{-}& {\mathrm{\Φ}}_{R_i}& {\mathrm{\Φ}}_{t_i}& {\mathrm{\Φ}}_{R_i}^{+}& {\mathrm{\Φ}}_{t_i}^{+}\end{array}\]\left\{\begin{array}{c}{\mathrm{\δR}}_{i-1}\\ {\mathrm{\δt}}_{i-1}\\ {\mathrm{\δR}}_i\\ {\mathrm{\δt}}_i\\ {\mathrm{\δR}}_{i+1}\\ {\mathrm{\δt}}_{i+1}\end{array}\right\}---\left(10\right)$

Wherein V_i=[v_xi,v_yi,v_zi], R_i=[x_i,y_i,z_i], V_i ^-Represent from X_i-1The speed that forward direction integration is obtained, and V_i ⁺Table Show from X_i+1Inversely integrate the speed for obtaining；

Speed amendment is carried out to every track section by formula (10), new initial position and every section of time of integration is obtained.

4. stable orbit computational methods of asynchronous binary-star system as claimed in claim 1, it is characterised in that：Described in step 2 Searching method include using speed Poincaré map or grid search.

5. stable orbit computational methods of asynchronous binary-star system as claimed in claim 1, it is characterised in that：Calculate each section of rail The method of position and velocity deviation between road is：The each fragment position error of track and velocity error of the new amendment of note is δ r_iWith δ v_i, rail The total site error in road is designated asGeneral speed error is designated as If δ is R ＜ ε₁And δ V ＜ ε₂Then think that track is continuous, as stable orbit, adjusted according to asteroidal size and task precision；If Constraint then repeat step four and five are unsatisfactory for, stable track is obtained by successive ignition.

6. stable orbit computational methods of the asynchronous binary-star system as described in claim 1 or 5, it is characterised in that：The ε₁, ε₂For in a small amount.

7. stable orbit computational methods of asynchronous binary-star system as claimed in claim 6, it is characterised in that：The ε₁=10^-5M, ε₂=10^-3m/s。